[SOLVED] Confusing Functions

I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

1) A piece of wire long has the shape of a rectangle. Given that the width is , show that the area, , of the rectangle is given by the function . Find the greatest possible domain and the corresponding range of this function in this context.

2) Sketch the graph of

Given that is the volume of a cuboid with height , length and , state an appropriate domain for the function given above.

Can you also please tell me how would I go on about sketching these kind of graphs.

I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

1) A piece of wire long has the shape of a rectangle. Given that the width is , show that the area, , of the rectangle is given by the function . Find the greatest possible domain and the corresponding range of this function in this context.

2) Sketch the graph of

Given that is the volume of a cuboid with height , length and , state an appropriate domain for the function given above.

Can you also please tell me how would I go on about sketching these kind of graphs.

Thanks in advance!

HI

(1) The width is w , then let the other side be x .

2x+2w=24 .... x+w=12

A=wx

A=w(12-w)

A=12w-w^2

A-36=12w-w^2-36

A-36=-(36-12w+w^2)

A-36=-(6-w)^2

A=36-(6-w)^2

When you graph this , it has an 'n' shape so w=6 and the correspoinding range would be 36 .